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A machine gun fires a bullet of mass 40 g with a velocity of $1200m{s}^{-1}$. The gun can exert a maximum force of 144 N on the bullet. How many bullets can it fire per second at the most?

(AIEEE 2004)

Two particles are released from the same height at an interval of 1 second how long after the first particle begins to fall will the two partocles be 10 m apart

A ball is thrown vertically downward with a velocity $u$ from the top of a tower. It strikes the ground with a velocity $5u$. The time taken by the ball to reach the ground is given by

A capacitor, of capacity $C$, is fully charged with voltage $V_0$. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance $\frac{C}{2}$. The energy loss in the process, after the charge is distributed between the two capacitors, is :

An aeroplane is travelling horizontally at a height of $2000\text{m}$ from the ground. The aeroplane, when at a point P, drops a bomb to hit a stationary target Q on the ground. In order that the bomb hits the target, what angle $\theta$ must the line PQ make with the vertical ? $[g=10m{s}^{-2}]$

A current I is passing through a wire having two sections P and Q of uniform diameters d and $\frac{d}{2}$ respectively. If the mean drift velocity of electrons in sections P and Q is denoted by $v_p$and $v_Q$respectively, then

A small block of mass $m$ is placed over a long plank of mass $M$. Coefficient of friction between them is $\mu$. Ground is smooth. At $t=0$, $m$ is given a velocity $v_1$ and $M$ a velocity $v_2(>v_1)$ as shown in the figure. After this $M$ is maintained at constant acceleration $a(<\mu g)$.



The forward force acting on the plank before and after $t_0$ respectively is

Two springs of spring constants 1500 N/m and 3000 N/m respectively are stretched with the same force. They will have potential energy in the ratio

Block B has a mass m and is released from rest when it is on top of wedge A, which has a mass 3 m. Determine the tension in cord CD needed to hold the wedge from moving while B is sliding down A. Neglect friction

Figure shows three concentric spherical conducting shells A, B, and C of radii $R,2R$ and $4R$ respectively. Shells $A$ and $C$ are connected by a conducting wire and B is given charge $Q$. $[\text{Consider}\frac{1}{4\pi {ϵ}_0}=K]$
Match the following columns:

$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{A. Charge on shell A}& \left(p\right)\frac{Q}{3}\\ \text{B. Charge on shell C}& \left(q\right)-\frac{Q}{3}\\ \text{C. Potential of shell A}& \left(r\right)Q\\ \text{D. Potential of shell C}& \left(s\right)\frac{KQ}{4R}\\ & \left(t\right)\text{None}\end{array}$

In the circuit given in the figure, switch S is closed at position 1 for long time. Find the total heat generated in resistor of resistance $2r_0$, when the switch S is open at position 1 and closed at position 2.

Lara has her baby weighed at an early childhood centre every four weeks. The uncertainty in the measurement is $50\text{g}$. When the baby gets four weeks old, its weight is measured as $3.20\text{kg}$. When he gets eight weeks old, its weight is measured as $4.05\text{kg}$. The baby's weight gain in this four week period is therefore:

A person travels along a straight road for the first half time with a velocity $v_1$ and the second half time with a velocity $v_2$. Then, the mean or average velocity $\overline{v}$ of the person is given by

A uniform force of $(3\hat{i}+\hat{j})\text{N}$ acts on a particle of mass $2\text{kg}.$ Hence the particle is displaced from position $(2\hat{i}+\hat{k})\text{m}$ to position $(4\hat{i}+3\hat{j}-\hat{k})\text{m}.$ The work done by the force on the particle is -

A cubical beaker of edge length $10\text{cm}$ is filled with a liquid of surface tension $0.075\text{N/m}$. Force across an imaginary diagonal on the surface of the liquid is

Suppose one object receives a charge q and the other Q-q, find the force between the objects.

For the given circuit, the average power developed is -

Compare the sounds made by a Cuckoo and roar of a Tiger. Which among these two have higher pitch and what quantity determines the pitch.Also give the unit of the quantity.

If the battery voltage in the figure is 12 volts and the plate separation is 0.8 cm. If a charge of 3 μC moves from the upper plate to the lower one, what is its change in electrical potential energy?

Two non-mixing liquids of densities $1000{\text{kg/m}}^3$ and $2000{\text{kg/m}}^3$ having height of $1\text{m}$ each are taken in a container, as shown in the figure. When a solid cylinder of length $0.5\text{m}$ and density $\rho$ is inserted in this container, it is observed that the cylinder floats with its axis being vertical and a length $0.2\text{m}$ of it in the denser liquid. The density $\rho$ of the solid cyclinder will be equal to